We propose a framework to address the problem of broadcasting a multiplicity of video sequences over a multiuser broadcast channel. The approach is intended to be general, without assumptions about specific video-coding or modulation techniques. However, we do assume the channel is Gaussian and exhibits quasi-static Rayleigh fading. Under the proposed framework, the algorithms seek to minimize the total distortion of multiple sequences broadcast simultaneously. To suit different applications, both greedy and long-term distortion metrics are considered. A salient aspect of this work is support for real-time video transport, hence delay and buffer constraints need to be accounted for. Under these constraints, the algorithms compute a jointly optimal source-rate and transmit-power allocation for all users under a power constraint. It turns out that problem can be formulated efficiently as a geometric program, which can be solved in different ways. In particular, we investigate a class of primal-dual convex algorithms. The complexity of the optimization is seen to scale well with the number of users. For the purpose of comparison, an orthogonal multiplexing scheme is also considered. Numerical results with H.264-coded video show that significant coding gains can be obtained.